Abstract: The importance of optics and is summarized in the 2013 US National Academy of Sciences report "Optics and Photonics: Essential Technology for Our Nation". Envisioned technologies which rely on optics include communications, imaging, sensing, and computing. What is clear from the report is that the Mathematical Sciences is poised to make significant contributions to the progress in technology. Indeed there is a growing research activity at the nexus of the Mathematical Sciences and the Optical Sciences. Together with advances in materials science and nano-structure fabrication, there is a growing role for mathematical tools, both computational and analytical.

The goal of this minisymposium is to highlight research in the mathematical sciences that deal with problems arising in optics and photonics. Topics that will be discussed in the sessions include optics in meta-materials, cloaking, photonic bandgap structures, design and control of optical devices, plasmonics, and nonlinear phenomena in optics. These topics will be emphasized during the Institute for Mathematics and its Applications (IMA) annual thematic program "Mathematics and Optics", 2016-17. The minisymposium is an invitation to mathematical scientists to participate in the IMA program.

MS-Th-E-18-116:00--16:30Spectral theory of Neumann-Poincar\'e operator and analysis of plasmon resonance
Kang, Hyeonbae (Inha Univ.)Abstract: The Neumann-Poincar\'e (NP) operator is a boundary integral operator which arises naturally when solving boundary value problems using layer potentials. It is not self-adjoint with the usual inner product. But it can symmetrized by introducing a new inner product using Plemelj's symmetrization principle. Recently many interesting properties of the NP operator have been discovered. I will discuss about this development and applications to plasmon resonance.

MS-Th-E-18-216:30--17:00Approximate cloaking via change of variablesNguyen, Hoai-Minh (Ecole Polytechnique Federale de Lausanne EPFL)Abstract: Cloaking using transformation optics was suggested by Pendry et al. and Leonhardt. A similar scheme was previously used by Greenleaf et al. for electrical impedance tomography. In this talk, I discuss approximate cloaking using transformation optics. Emphasis is on the occurence of the resonance and the cloaking on the time domain. The approximate schemed considered is due to Kohn et al.

MS-Th-E-18-317:00--17:30Vertical mode expansion method for electromagnetic scattering problemsLu, Ya Yan (City Univ. of Hong Kong)Abstract: In many applications, it is necessary to solve the 3D Maxwell's equations for scattering problems where the scatter is a layered cylindrical object in a layered background. The vertical mode expansion method (VMEM) is a recently developed method that expands the field in 1D modes with "coefficients" satisfying 2D Helmholtz equations, and finds the solution by matching field components along the boundaries of different layered regions. We present the VMEM with applications in plasmonics.

MS-Th-E-18-417:30--18:00Spectral theory in the absence of ellipticity for high contrast photonic crystalsLipton, Robert (LSU)Viator, Robert (Louisiana State Univ.)Abstract: Photonic crystals employ high contrast media for controlling light. Here we identify an underlying quasiperiodic resonance spectra and use it to represent solution operators associated with the Maxwell system for high contrast photonic crystals. We develop representation formulas for the resolvent for selfadjoint holomorphic families of operators. This technique is applied to compute and to design dispersion characteristics for photonic crystals. Computational examples of this approach are provided to illustrate the ideas.